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The Octopus computer network at the Lawrence Livermore Laboratory, University of California, Livermore, ties together one of the largest concentrations of computing capability in the world, serving about 1500 users. The network's information storage capacity is large in every range of access speed. There are computers with main memories of 30 Mbits and secondary storage of 10 Gbits, a shared tertiary store of 1 Tbit, and 30-40 thousand reels of magnetic tape. This storage supports correspondingly large numerical simulations and other application programs that require the continuous operation of four major computers. Efficient storage use necessitates proper design of algorithms and buffer structures on the part of both the users and the system implementors. The main problems that arise include maintenance of high data transfer rates, reliability in the presence of intermittent hardware failure, achieving balance between media with differing access speeds, flexibility of the indexing structure, and equitable allocation among users. The discussion covers these issues in some detail and includes an historical perspective and estimates of future trends.